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An explicit parametrization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system is presented. These results are used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.
If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.
Bounds for the linear feedback capacity of m-th order Gaussian autoregressive channels are derived. The upper bound is tighter than that found by Tiernan and Schalwijk (1974) for the feedback capacity of a first-order autoregressive Gaussian channel with not necessarily linear processing. The separation between the upper and lower bounds is small, and it is conjectured that the lower bound converges to the feedback capacity of the first-order channel as the number of signals tends to infinity.
This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.
A procedure is derived for stabilizing linear constant discrete systems which is a discrete analog to the extended Bass algorithm for stabilizing linear constant continuous systems. The procedure offers a method for constructing a stabilizing feedback without the computational difficulty of raising the unstable open-loop response matrix to powers thus making the method attractive for high order or poorly conditioned systems.
This paper contains an explicit parametrization of a subclass of linear constant gain feedback maps that will not destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Optimal filtering equations are obtained for very general linear stochastic delay systems. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.
A method is presented which transforms certain nonlinear differential equations of dynamics into linear equations by introducing an independent variable and utilizing the integrals of motion. As examples of special interest, the linearizations of unperturbed and perturbed Keplerian motions are discussed.
The propagation of sound in a converging-diverging duct containing a quasi-one-dimensional steady flow with a high subsonic throat Mach number is studied. The behavior of linearized acoustic theory at the throat of the duct is shown to be singular, and the explicit form of the singularity is determined for two special types of area variation. Numerically computed results showing the development of the singularity are presented. The singularity implies that linearized acoustic theory is invalid for sound propagating through a throat carrying a near-sonic flow.
A description is presented of a dual-fuel modular split-combustor linear aerospike engine concept. The considered engine represents an approach to an integrated engine for a reusable single-stage-to-orbit (SSTO) vehicle. The engine burns two fuels (hydrogen and a hydrocarbon) with oxygen in separate combustors. Combustion gases expand on a linear aerospike nozzle. An engine preliminary design is discussed. Attention is given to the evaluation process for selecting the optimum number of modules or divisions of the engine, aspects of cooling and power cycle balance, and details of engine operation.
Results obtained in the first part of this paper (1976), which studied forced baroclinic ocean motions in the linear equatorial unbounded case, are extended to the case of an ocean bounded by two meridians. A complete solution for the linear spin-up in response to a switched-on, x-dependent wind stress is obtained in terms of five components: the unbounded nonoscillatory response to the wind stress forcing; the inertia-gravity waves generated when the forcing switches on, together with their reflections; the quasi-geostrophic Rossby modes forming the eastern boundary response and a western boundary layer; and the equatorial Kelvin wave component of the western boundary response. Kelvin waves are generated if the forcings include a zonal wind component that is symmetric about the equator or an antisymmetric meridional wind stress. For non-Kelvin symmetries, spin-up occurs entirely by the effects of Rossby waves emanating from the eastern boundary. The state approaches the steady solution as increasing numbers of these reach an interior point. In Kelvin symmetries, the Rossby waves act to bring the sea surface tilt to the steady value and the spin-up of the tilt proceeds as in non-Kelvin cases.
The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.
Control-theory design package aids design of linear-quadratic-Gaussian (LOG) controllers and optimal filters. It is applicable to systems that can be modeled by linear time-invariant differential or difference equations.
Parametric data on split-combustor linear engine propulsion systems are presented for use in mixed-mode single-stage-to-orbit (SSTO) vehicle studies. Preliminary design data for two selected engine systems are included. The split combustor was investigated for mixed-mode operations with oxygen/hydrogen propellants used in the inner combustor in Mode 2, and in conjunction with either oxygen/RP-1, oxygen/RJ-5, O2/CH4, or O2/H2 propellants in the outer combustor for Mode 1. Both gas generator and staged combustion power cycles were analyzed for providing power to the turbopumps of the inner and outer combustors. Numerous cooling circuits and cooling fluids (propellants) were analyzed and hydrogen was selected as the preferred coolant for both combustors and the linear aerospike nozzle. The maximum operating chamber pressure was determined to be limited by the availability of hydrogen coolant pressure drop in the coolant circuit.
A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.
A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.
The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.
Astronauts, particularly in Skylab flights, experienced varying degrees of motion sickness lasting 3-5 days. One possible mechanism for this motion sickness adaptation is believed to be a reduction in otolith sensitivity with an attendant reduction in sensory conflict. In an attempt to determine if this hypothesis is valid, a ground-based pilot study was conducted on a vertical linear accelerator. The extent of habituation to accelerations which initially produced motion sickness was evaluated, along with the possible value of habituation training to minimize the space motion sickness problem. Results showed that habituation occurred for 6 of the 8 subjects tested. However, in tests designed to measure dynamic and static otolith function, no significant differences between pre- and post-habituation tests were observed. Cross habituation effects to a standard Coriolis acceleration test were not significant. It is unlikely that ground-based pre-habituation to linear accelerations of the type examined would alter susceptibility to space motion sickness.